MCAT topics → Translational Motion, Forces, Work, and Energy → Power

Power

MCAT trap: Conflates total work done with power, ignoring the time component. Power is work per unit time (P = W/t); an engine doing less work in much less time can have greater power than one doing more work slowly.

Power is the rate at which work is done — P = W/t, and equivalently P = Fv for a constant force. The MCAT tests this in mechanics passages involving engines, elevators, pumps, and people climbing stairs, and also in circuits where P = IV. The most common error: treating high total work output as automatically meaning high power. It does not — power depends on how fast that work is done. A small motor doing 100 J in 0.1 s (1000 W) is far more powerful than a large engine doing 1000 J in 100 s (10 W).

The exam hits power from three angles: definitional recall (know both formulas cold), calculation (plug in force and velocity, or work and time, for real-world machines), and cross-disciplinary connection (recognize that a watt is a watt whether you're talking about a motor or a resistor). Passage-based questions will often give you a scenario where an engine outputs a certain force at a certain speed and ask you to compare power outputs — the trap is always ignoring time.

The trickiest part is keeping energy and power conceptually separate. Both formulas — P = W/t and P = Fv — look simple, but students frequently treat a high-work output as automatically meaning high power, or they treat watts and joules as the same thing. On the MCAT, precision about units is often the difference between the right answer and a trap answer.

Common misconceptions

Common mistake
Wrong: An engine that does more work always has more power than one that does less work.
Right: Power is work per unit time (P = W/t); an engine doing less work in much less time can have greater power than one doing more work slowly.
Total work done tells you nothing about power on its own — you must know how long it took. A small motor doing 100 J in 0.1 s (1000 W) is far more powerful than a large engine doing 1000 J in 100 s (10 W). Always ask: work divided by what time? Power is about rate, not totals.
Common mistake
Wrong: P = Fv applies only when the object is accelerating.
Right: P = Fv gives instantaneous power for any force F acting on an object moving at velocity v, regardless of whether the object is accelerating.
P = Fv is an instantaneous power formula that works any time a force F acts on an object moving at speed v, whether or not the net force is zero. If you're pushing a box at constant velocity, P = Fv still gives the power you're delivering. The formula says nothing about acceleration — it's about how much force you're applying and how fast the object is moving at that instant.
Common mistake
Wrong: Watts and joules are interchangeable units for energy.
Right: Joules measure energy (or work), while watts measure power (joules per second); they are related by W = P × t.
Joules and watts measure fundamentally different things: joules are energy (or work), watts are energy per second. They're connected by W = P × t, meaning you need both a power level and a duration to get an energy amount. A 100 W lightbulb running for 10 seconds uses 1000 J of energy — those numbers are not interchangeable.
Free Deck audit

See if your Anki deck covers this topic.

Upload your deck →
Guided session

Stuck on this? An AI tutor that probes your understanding.

Start a session →

What the exam tests

  1. Know both definitions of power: P = W/t (work per unit time) and P = Fv (force times velocity), and recognize when to use each.
  2. Calculate power output for engines, pumps, or people given any combination of force, velocity, work, and time — including unit conversions between watts and kilowatts.
  3. Connect mechanical power (watts = J/s) to electrical power (P = IV) and recognize that a watt is the same unit regardless of context, bridging physics and circuits.

Can you avoid these mistakes?

A person lifts a 60 kg box 2 meters in 3 seconds. What is their average power output? (g = 10 m/s²)
An engine exerts a constant 500 N force on a car moving at 20 m/s. What is the engine's power output, and does your answer change if the car is at constant velocity versus accelerating?
Engine A does 10,000 J of work in 5 seconds. Engine B does 6,000 J in 2 seconds. Which engine has greater power, and by how much?
A circuit element dissipates 60 W. A mechanical pump also outputs 60 W. How are these the same, and what formula connects power to energy for both?

Related topics

Work and the Work-Energy Theorem One-Dimensional Kinematics Two-Dimensional Kinematics and Projectile Motion Newton's Three Laws of Motion Friction (Static and Kinetic)

See how your Anki deck covers this topic.

Upload your deck for a free audit →